1. Problem 2: A cone, 50 mm base diameter and 70 mm axis is
standing on it’s base on Hp. It cut by a section plane 450 inclined
to Hp through base end of end generator.Draw projections,
sectional views, true shape of section and development of surfaces
of remaining solid.
Solution Steps:for sectional views:
Draw three views of standing cone.
Locate sec.plane in Fv as described.
Project points where generators are
getting Cut on Tv & Sv as shown in
illustration.Join those points in
sequence and show Section lines in it.
Make remaining part of solid dark.
TRUE SHAPE OF SECTION X1 Y1 A
SECTIONAL S.V o’ B
SECTION
PLANE
DEVELOPMENT C D E a’ b’ d’ e’ c’ g’ f’ h’ X
g” h”f” a”e” b”d” c” Y F h a b c d e g f
For True Shape:
Draw x1y1 // to sec. plane
Draw projectors on it from
cut points.
Mark distances of points
of Sectioned part from Tv,
on above projectors from
x1y1 and join in sequence.
Draw section lines in it.
It is required true shape. G
For Development:
Draw development of entire solid.
Name from cut-open edge i.e. A.
in sequence as shown.Mark the cut points on respective edges.
Join them in sequence in curvature. Make existing parts dev.dark. H A
SECTIONAL T.V

2. Problem 3: A cone 40mm diameter and 50 mm axis is resting on one generator on Hp( lying on Hp) which is // to Vp.. Draw it’s projections.It is cut by a horizontal section plane through it’s base center. Draw sectional TV, development of the surface of the remaining part of cone.
Follow similar solution steps for Sec.views - True shape – Development as per previous problem!
DEVELOPMENT o’ A B C D E F G H
HORIZONTAL
SECTION PLANE a’
h’b’ e’
c’g’
d’f’ X e’ a’ b’ d’ c’ g’ f’ h’ o’ Y O h a b c d e g f O a1 h1 g1 f1 e1 d1 c1 b1 o1
SECTIONAL T.V
(SHOWING TRUE SHAPE OF SECTION)

3. Problem 5:A solid composed of a half-cone and half- hexagonal pyramid is
shown in figure.It is cut by a section plane 450 inclined to Hp, passing through
mid-point of axis.Draw F.v., sectional T.v.,true shape of section and
development of remaining part of the solid.
( take radius of cone and each side of hexagon 30mm long and axis 70mm.) 7 1 6 5 4 3 2
TRUE SHAPE X1 Y1
Note:
Fv & TV 8f two solids
sandwiched
Section lines style in both:
Development of
half cone & half pyramid: O’ A B C D E F G O
DEVELOPMENT 1’ 2’ 3’ 4’ 5’ 6’ 7’
F.V. 4 5 3 6 2 7 1 X Y
d’e’
c’f’
g’b’ a’ a b c d e f g 7 1 5 4 3 2 6
SECTIONAL
TOP VIEW.

4. =  +  TO DRAW PRINCIPAL VIEWS FROM GIVEN DEVELOPMENT. X Y
Problem 6: Draw a semicircle 0f 100 mm diameter and inscribe in it a largest
circle.If the semicircle is development of a cone and inscribed circle is some
curve on it, then draw the projections of cone showing that curve. A B C D E F G H O  = R L +
3600
R=Base circle radius.
L=Slant height. o’ 1 3 2 4 7 6 5 L 1’ 2’ 3’ 4’ 5’ 6’ 7’  X Y a’ b’ c’ g’
d’f’ e’ h’ L h a b c d g f o e 1 2 3 4 5 6 7
Solution Steps:
Draw semicircle of given diameter, divide it in 8 Parts and inscribe in it
a largest circle as shown.Name intersecting points 1, 2, 3 etc.
Semicircle being dev.of a cone it’s radius is slant height of cone.( L )
Then using above formula find R of base of cone. Using this data
draw Fv & Tv of cone and form 8 generators and name.
Take o -1 distance from dev.,mark on TL i.e.o’a’ on Fv & bring on o’b’
and name 1’ Similarly locate all points on Fv. Then project all on Tv
on respective generators and join by smooth curve.

5. =  +  TO DRAW PRINCIPAL VIEWS FROM GIVEN DEVELOPMENT. X Y
Problem 6: Draw a semicircle 0f 100 mm diameter and inscribe in it a largest
circle.If the semicircle is development of a cone and inscribed circle is some
curve on it, then draw the projections of cone showing that curve. A B C D E F G H O  = R L +
3600
R=Base circle radius.
L=Slant height. o’ 1 3 2 4 7 6 5 L 1’ 2’ 3’ 4’ 5’ 6’ 7’  X Y a’ b’ c’ g’
d’f’ e’ h’ L h a b c d g f o e 1 2 3 4 5 6 7
Solution Steps:
Draw semicircle of given diameter, divide it in 8 Parts and inscribe in it
a largest circle as shown.Name intersecting points 1, 2, 3 etc.
Semicircle being dev.of a cone it’s radius is slant height of cone.( L )
Then using above formula find R of base of cone. Using this data
draw Fv & Tv of cone and form 8 generators and name.
Take o -1 distance from dev.,mark on TL i.e.o’a’ on Fv & bring on o’b’
and name 1’ Similarly locate all points on Fv. Then project all on Tv
on respective generators and join by smooth curve.

6. = X Y   + TO DRAW PRINCIPAL VIEWS FROM GIVEN DEVELOPMENT.
Problem 7:Draw a semicircle 0f 100 mm diameter and inscribe in it a largest
rhombus.If the semicircle is development of a cone and rhombus is some curve
on it, then draw the projections of cone showing that curve.
Solution Steps:
Similar to previous
Problem: o’ A B C D E F G H O 1’ 2’ 3’ 4’ 5’ 6’ 7’ a’ b’ d’ c’ g’ f’ h’ e’ X Y  h a b c d g f e L 1 2 3 4 5 6 7  = R L +
3600
R=Base circle radius.
L=Slant height.

7. TO DRAW A CURVE ON PRINCIPAL VIEWS FROM DEVELOPMENT.
Problem 8: A half cone of 50 mm base diameter, 70 mm axis, is standing on it’s half base on HP with it’s flat face
parallel and nearer to VP.An inextensible string is wound round it’s surface from one point of base circle and
brought back to the same point.If the string is of shortest length, find it and show it on the projections of the cone.
TO DRAW A CURVE ON
PRINCIPAL VIEWS
FROM DEVELOPMENT.
Concept: A string wound
from a point up to the same
Point, of shortest length
Must appear st. line on it’s
Development.
Solution steps:
Hence draw development,
Name it as usual and join
A to A This is shortest
Length of that string.
Further steps are as usual.
On dev. Name the points of
Intersections of this line with
Different generators.Bring
Those on Fv & Tv and join
by smooth curves.
Draw 4’ a’ part of string dotted
As it is on back side of cone. a’ b’ c’ d’ o’ e’ A B C D E O 2 3 4 1 1’ 2’ 3’ 4’ X Y a b c d o e 1 2 3 4